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Affine processes under parameter uncertainty

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  • Tolulope Fadina
  • Ariel Neufeld
  • Thorsten Schmidt

Abstract

We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programming principle we link this non-linear expectation to a variational form of the Kolmogorov equation, where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in the parameter set. This non-linear affine process yields a tractable model for Knightian uncertainty, especially for modelling interest rates under ambiguity. We then develop an appropriate Ito-formula, the respective term-structure equations and study the non-linear versions of the Vasicek and the Cox-Ingersoll-Ross (CIR) model. Thereafter we introduce the non-linear Vasicek-CIR model. This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence the approach solves this modelling issue arising with negative interest rates.

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  • Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    • Handle: RePEc:arx:papers:1806.02912
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
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    3. Denk, Robert & Kupper, Michael & Nendel, Max, 2019. "A Semigroup Approach to Nonlinear Lévy Processes," Center for Mathematical Economics Working Papers 610, Center for Mathematical Economics, Bielefeld University.
    4. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
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    Cited by:

    1. Schmidt, Thorsten & Tappe, Stefan & Yu, Weijun, 2020. "Infinite dimensional affine processes," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7131-7169.

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